Parallelogram 11 • Level 4 • 16 Nov 2023A Beautiful Mind
Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/
- a portmanteau word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.
- Tackle each Parallelogram in one go. Don’t get distracted.
- Finish by midnight on Sunday if your whole class is doing parallelograms.
- Your score & answer sheet will appear immediately after you hit SUBMIT.
- Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.
1. What is the zeroth power?
This video is from the Khan Academy, which is a great resource for learning about mathematics and many other things. You can watch videos via their website, or via YouTube. This video explains what happens when you raise a number to the power zero, and it gives two reasons for the result.
(If you have problems watching the video, right click to open it in a new window)1.1. What is 90?
Correct Solution: 1
1.2. What is 03?
Correct Solution: 0
2. A Beautiful Mind
“A Beautiful Mind” is an Oscar-winning film about the mathematician John Nash, who won a Nobel Prize in Economics. It’s a great film and definitely worth watching, but maybe wait until you are a bit older.
This clip shows a grumpy Nash teaching a class in mathematics, and a young student (who later married him) shows him that there can be more than one solution to a problem.
(If you have problems watching the video, right click to open it in a new window)2.1. Here is another problem with two solutions. Look at these four equations. Try to work out the rule from the first three equations, and then work out the value of (?). First, find the answer that is less than 50.
1 + 4 = 5
2 + 5 = 12
3 + 6 = 21
8 + 11 = ?
In the 2nd line, (2 + 5 ≠ 12), but what about adding the answer to 1st line to (2 + 5)?
In the 3rd line, (3 + 6 ≠ 21), but what about adding the answer to 2nd line to (3 + 6)?
Correct Solution: 40
In order to make each line correct, you need to add the number from the previous line.
In the 2nd line, (2 + 5 ≠ 12), but add 5 from the 1st line and (2 + 5 + 5 = 12).
In the 3rd line, (3 + 6 ≠ 21), but add 12 from the 2nd line and (3 + 6 + 12 = 21).
In the 4th line, the answer is (8 + 11 + 21) = 40.
2.2. Now find the answer that is more than 50, which will require a different rule.
This rule requires you to multiply both numbers and add the first one. For example:
In the 2nd line, (2 + 5 ≠ 12), but (2 × 5 + 2 = 12).
In the 3rd line, (3 + 6 ≠ 21), but (3 × 6 + 3 = 21).
Correct Solution: 96
This rule requires you to multiply both numbers and add the first one. For example:
In the 2nd line, (2 + 5 ≠ 12), but (2 × 5 + 2 = 12).
In the 3rd line, (3 + 6 ≠ 21), but (3 × 6 + 3 = 21).
So, in line 4, (8 + 11) means (8 × 11 + 8 = 96).
3. Intermediate Maths Challenge Problem (UKMT)
3.1 Merlin magically transforms a 6 tonne monster into mice with the same total mass.
Each mouse has a mass of 20g. How many mice does Merlin make?
- 30
- 300
- 3,000
- 30,000
- 300,000
- (Not answered)
1 tonne = 1000 kg = 1000 × 1000 g, so 6 tonnes = 6 × 1000 × 1000 g . So the number of 20 g mice that Merlin makes is:
(6 × 1000 × 1000)/20 = 6 × 1000 × 50 = 6 × 50,000 = 300,000.
Before you hit the SUBMIT button, here are some quick reminders:
- You will receive your score immediately, and collect your reward points.
- You might earn a new badge... if not, then maybe next week.
- Make sure you go through the solution sheet – it is massively important.
- A score of less than 50% is ok – it means you can learn lots from your mistakes.
- The next Parallelogram is next week, at 3pm on Thursday.
- Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.
Cheerio, Simon.